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Simplifying 75 = x2 + -30x Reorder the terms: 75 = -30x + x2 Solving 75 = -30x + x2 Solving for variable 'x'. Reorder the terms: 75 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 75 + 30x + -1x2 = 0 + x2 + -1x2 75 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + -30x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -30x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -30x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -30x + x2 = 0 + 75 -30x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -30x + x2 = 75 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 75 + 225 Reorder the terms: 225 + -30x + x2 = 75 + 225 Combine like terms: 75 + 225 = 300 225 + -30x + x2 = 300 Factor a perfect square on the left side: (x + -15)(x + -15) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + -15) equal to 17.320508076 and -17.320508076.Subproblem 1
x + -15 = 17.320508076 Simplifying x + -15 = 17.320508076 Reorder the terms: -15 + x = 17.320508076 Solving -15 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 17.320508076 + 15 Combine like terms: -15 + 15 = 0 0 + x = 17.320508076 + 15 x = 17.320508076 + 15 Combine like terms: 17.320508076 + 15 = 32.320508076 x = 32.320508076 Simplifying x = 32.320508076Subproblem 2
x + -15 = -17.320508076 Simplifying x + -15 = -17.320508076 Reorder the terms: -15 + x = -17.320508076 Solving -15 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -17.320508076 + 15 Combine like terms: -15 + 15 = 0 0 + x = -17.320508076 + 15 x = -17.320508076 + 15 Combine like terms: -17.320508076 + 15 = -2.320508076 x = -2.320508076 Simplifying x = -2.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.320508076, -2.320508076}
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